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3 years ago

vector w has magnitude 25.0 and direction angle 41.7 degrees. Calculate the horizontal and vertical components of w

Mathematics

1 answer:

11Alexandr11 [23.1K]3 years ago

5 0

Consider the attached picture. It represents a vector, centered in the origin with angle 41.7 degrees, and a circumference with radius 25, centered in the origin.

As you can see, the horizontal and vertical components of the vector correspond to the lengths of segments OD and OC, respectively.

You might recognize this scenario from you trigonometry class: if the circle had radius 1, we would have

$OD=\cos(41.7),\quad OC=\sin(41.7)$

Since the circle has radius 25, we have to scale those coordinates:

$OD=25\cos(41.7),\quad OC=25\sin(41.7)$

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To find the equation of the line, we are going to use the point-slope form, which is listed below:

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You may notice that we have a point, but no slope is given to us. However, the problem states that the line is parallel to the equation $y = 3x + 7$ , which means that it has the same slope as this line, which is 3. (Remember that this line is set up in $y = mx + b$ form, where $m$ is the slope)

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The problem made it clear that it didn't want the form $y = 3x - 13$ , so let's put it in standard form:

$y = 3x - 13$

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Answer:

$\sf \text{The numbers are $\dfrac{-14}{3} $ and $\dfrac{-7}{3}$}$

Step-by-step explanation:

Let the numbers be x , y

Sum of two numers = -7

x + y = -7------------(I)

Two times the first number equals 4 the second number.

2x = 4y ----------(II)

Divide both sides by 2

$\sf \dfrac{2x}{2}=\dfrac{4y}{2}$

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Subtitute x = 2y in equation (I)

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Plugin y = -7/3 in equation (II)

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